Method for linearizing deflection of a mems device using binary electrodes and voltage odulation

ABSTRACT

A micromechanical device comprising one or more electronically movable structure sets comprising for each set a first electrode supported on a substrate and a second electrode supported substantially parallel from said first electrode. Said second electrode is movable with respect to said first electrode whereby an electric potential applied between said first and second electrodes causing said second electrode to move relative to said first electrode a distance X, (X), where X is a nonlinear function of said potential, (V). Means are provided for linearizing the relationship between V and X.

CROSS REFERENCE TO RELATED APPLICATIONS

The present invention claims priority to U.S. Provisional ApplicationSer. No. 60/363,139 commonly owned with the application.

STATEMENT REGARDING FEDERALY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government Support under Contract NumberW-7405-ENG-48 awarded by the Department of Energy. The Government hascertain rights in the invention.

BACKGROUND OF THE INVENTION

Among the applications for micromechanical devices are planar actuatorscomprising one or typically an array of actuators in a two-dimensionalmatrix in which individual elements of the array need to be individuallyand rapidly displaced.

In one application of such actuators to the deflection of radiation, anarray of actuators includes mirrors activated by micromechanicalelectrostatic motivators to provide rapid displacement of the mirrorpositions in the array in order to alter the phase delay of incomingradiation wavefronts and thereby adjust the phase of the reflected lightor the angle of reflection.

In modern high-speed systems such as scanners and pattern recognitionsystems, the demands for rapid adjustment of the phase of reflectedlight or beam angle continue to increase, placing severe demands uponcontrol circuitry for an array of large dimensions to precisely andindividually control each of hundreds or thousands of mirror elements inthe array.

An additional problem encountered in controlling such actuators is thenonlinearity between displacement and applied control voltage due to themathematical relationship between displacement and applied potential inwhat is essentially a parallel-plate capacitor geometry. To deal withthe nonlinearity in order to provide accurate beam reflection, a heavydemand is placed upon processing electronics to accomplish anyadjustment to the hundreds or thousands of individual actuators forcontrolling the position on an ongoing, rapid sequence basis.

BRIEF SUMMARY OF THE INVENTION

The present invention provides for an effective way of linearizing theresponse between desired position and applied potential that takesadvantage of and places structured designs directly into themicromechanical structure. It is operative directly in response todigital signals, avoiding the complexity and delay of looped processingto accomplish the mathematical linearization.

According to the present invention, at least one electrode of each ofthe parallel plate actuator elements is divided into a plurality ofelectrode segments of varying area, from a minimum first area to amaximum, nth area of greatest value, through a plurality of areasincreasing from one to the other by a factor of two. Each of theelectrode segments is individually addressed through voltage gates thatare controlled by binary ones and zeroes directly representative of theapplied voltage potential. The resulting nonlinear transfer functionthat relates the applied potential to the effective displacement causedby the applied potential counteracts some or all of the nonlinearity inthe relationship or transfer function between applied potential andactuator displacement.

The nonlinearity in the transfer characteristic between appliedpotential and actuator displacement is completely eliminated byadjusting the applied voltage that is applied to each of the electrodesegments through the use of a plurality of current sources each ofmagnitude varying from a low minimum first magnitude corresponding toand activated with activation of the first electrode segment andvarying, one to the other, by factor of two up to the largest or nthcurrent source, corresponding to and activated simultaneously withactivation of the largest or nth electrode segment.

The resulting system utilizes a simple structure not requiringtime-consuming electronic processing of the applied potential in orderto produce a linear relationship between displacement and input value,but nevertheless linearizing its relationship with respect to thedisplacement value it causes.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is more fully understood with respect to thedrawings of which:

FIGS. 1A and 1B are perspective views of first and second examples of aplanar actuator of the type to which the present invention is applied;

FIG. 2 is a schematic diagram of a single element of an actuator arrayof the type illustrated in FIGS. 1A and 1B;

FIGS. 3A and 3B are graphs representing the transfer function betweenthe desired deflection represented by either a voltage or a digitalnumber versus the actual displacement in an actuator of the typeillustrated in FIG. 2, being respectively nonlinear and linearizedtransfer functions.

FIG. 4 is a diagram illustrating the operation of a planar array inreflecting the rays of a light beam;

FIG. 5 is a schematic diagram illustrating a circuit according to theinvention for controlling individual actuator elements of a planaractivator array;

FIG. 6 illustrates the linearization of the transfer function relatingthe digital input signal and the displacement;

FIG. 7 is a diagrammatic illustration of a system for controlling aplanar array using circuitry of the type illustrated in FIG. 5.

DETAILED DESCRIPTION

FIGS. 1A and 1B illustrate planar arrays of actuators typical of thosein which the present invention is operative. Each array includes asubstrate 12 having thereon electrodes 14 on an insulating layer 13. Intypical micromechanical versions of the arrays, the substrate 12 issilicon, the insulating layer 13 silicon nitride, and electrodes 14 maybe either metalizations or conductive diffusions, each with appropriateleads, typically metalizations, not shown to apply potential thereto.Above the substrate 12 a plurality of second electrodes 16 are supportedby legs 18 in the case of FIG. 1A or monolithic structures 20 in thecase of FIG. 1B. In the case of FIG. 1A, the electrodes 14 may becommonly connected whereas the second electrodes 16 are individuallymetallized and connected by supports 18 to individual circuit leads. Inthe case of FIG. 1B, the first electrodes 14 will typically beindividually connected to circuit leads while the electrodes 16 arecommonly connected to a single lead.

A reflective surface 22 is fastened above the second electrodes 16 viaposts 24 in both versions of FIGS. 1A and 1B.

FIG. 2 illustrates in cross-section a single actuator 26 from the planararray illustrated in FIG. 1B. In this case, the bottom electrodes 14 areindividually connected through leads not shown to individuallycontrolled sources of potential, such as the exemplary voltage source28, while the second, upper electrodes 16 are connected in commonthrough supports 20, typically to ground 30. The dimensions illustratedin FIG. 2 are exemplary only to identify the scale of the structures ofmicromechanical devices of this type and are not to be seen as limiting.

The force created by the voltage source 28, shown only for purposes ofillustration of operation of such activators, produces along illustratedelectrostatic field lines 32 a force between the electrodes 14 and 16.As the voltage increases, the force increases, and the displacement inthe direction X of the electrode 16 toward the electrode 32 increases.The relationship for such a structure is illustrated by the graph ofFIG. 3A which shows a typical transfer function between applied voltageV and displacement X. The curve 36 representing that transfer functionis dramatically nonlinear reflective of the fact that as the electrode16 approaches the electrode 14, the force due to the applied voltageincreases such that for every unit increase in applied voltage theresulting displacement becomes larger than the displacement for units atlower levels of applied voltage. Such a situation makes for acomplication in the ability to accurately control, typically in an openloop function such as in an image processor, the reflected phase orangle of deflection of an incident light beam.

FIG. 4 illustrates for such a typical array 26 the physics of light beamreflection. As shown in this example, an incident beam 40 of radiationis reflected by the reflective or mirror elements 22 creating an outputbeam 42. The input beam 40 has a wavefront 44 representing the locus ofsame phase radiation in the input beam 40. The output beam 42 has awavefront 46 again representing a locus of identical phase in the outputbeam 42. In an unactivated situation the mirrors 22 lie in the sameplane but diverge when activated by the application of a potentialindividually between the electrodes 14 and 16 of each actuator in array26. Upon activation selectively of the mirrors 22 by applyingrespectively different voltages between the electrodes 14 and 16, thepath length of the input beam and the output beam 42 can be varied overthe entire area of the wavefront 44 delaying some sections relative toother sections which in turn causes the output beam wavefront 46 to bechanged in phase resulting in a change in the phase of selected sectionsof the output beam itself.

In order to change or steer the input beam 40 onto differenttrajectories for output beams 42 it is essential that a progressivechange in displacement occur over the entire array of mirrors 22. Toaccomplish that accurately with the transfer function illustrated inFIG. 3A requires an enormously complex processing scheme if it is doneelectronically before the application of the individual voltages Vbetween the electrodes 14 and 16. The present invention linearizes theeffect of the applied voltage such that a transfer function between adigital number representing the desired deflection and the actualdisplacement 50 as illustrated in FIG. 3B is achieved. This isaccomplished using a circuit of the type shown in FIG. 5 which can besubstantially integral with the micromechanical structure and thus doesnot require time-consuming electronic processing that would reduce theresponse speed of the structure.

As illustrated in FIG. 5, each of the electrodes 14 is segmented into aplurality of electrode segments 60, 62 . . 64 each of increasing areawith a ratio of increase between each successively larger segment beinga factor of two, from the smallest, first electrode segment 60 to thelargest, nth electrode segment 64. While FIG. 5 illustrates only threeelectrode segments 60-64 it is to be understood in the application ofthe invention to a real structure there could be a larger number ofelectrode segments depending upon the desired resolution and theacceptable expense for the array and distribution circuitry to convertthe incoming voltage, typically in digital binary form to separate onesand zeroes for each electrode segment 60-64 application lead 66. Eachlead 66 is fed with a signal from corresponding data lines 70, 72 and74. For example, if an 8-bit data word or byte is used, representing 256possible data states or voltage levels, there will be eight electrodesegments 60-64 and corresponding data leads 70-74 corresponding to theindividual zero and one bit positions in the data word. By activating aselect combination of the electrode segments it is possible to achievethe corresponding voltage effect in 256 resolution steps. The digitalones and zeroes operate through control switches 80, 82 and 84 which maybe integral to the structure. The digital ones and zeroes representingthe desired deflection of said actuator 20 are carried on input lines70,72,74 and are obtained from the output of a digital control devicesuch as a computer, microprocessor, microcontroller, or logic circuit.The number of digital bits of said digital signal corresponds to thenumber of electrodes 60-64 included in the system. Each of the switches80-92 is activated by one digital line 70,72,74 of the digital signal,with the line 70 corresponding to the least significant bit (LSB)connected to the switch 80 and, in turn, the electrode segment ofsmallest area, and the line 74 corresponding to the most significant bit(MSB) connected to the switch 84 and, in turn, the nth electrode segmentof largest area.

The effect of the linearization achieved through the use of switches80-84 is to linearize the transfer function illustrated in FIG. 3A tothe form illustrated by curve 90 in FIG. 6. This is linearized to theextent that the curve is substantially flattened and can be adjusted tohave end points fitted to the end points of a fully linearized transferfunction illustrated by curve 92.

To achieve a linearization corresponding to the curve 92 an adjustmentin the reference voltage corresponding to the same digital word isprovided by applying a varying load in the form of current sources 100,102 and 104, connected via switches 101, 103, and 105 to a junctionpoint 106 common with the application of voltage V_(o) from a source 108through a resistor 110. The sources 100, 102, 104 are connected to thecommon junction point 106 by switches 101, 103, and 103 controlledthrough the same digital lines controlling the switches 80-84. Themagnitude of the current of each current source increases according to aseries from a first current of lowest value corresponding to the LSB andthe smallest electrode segment, increasing by a factor of two fromcurrent source to current source to the largest, nth current sourcecorresponding to the MSB and largest area electrode segment. In thismanner, a total linearization of the transfer function as illustrated incurve 92 can be achieved.

The mathematics corresponding to this linearization operate as follows:

Mechanical restoring force for a given displacement of the actuatorelectrode:FM=−kx  (1)where k is a mechanical spring constant and x the displacement.

Electrostatic force for a given applied voltage: $\begin{matrix}{F_{E} = \frac{{\varepsilon A}_{TOT}V^{2}}{2\left( {g - x} \right)^{2}}} & (2)\end{matrix}$where g is the spacing between electrodes 14 and 16 at zero appliedvoltage, A_(TOT) their area of overlap as seen from a view perpendicularto the surface, and ε a physical constant called the permittivity.

Equilibrium occurs when F_(M)+F_(E)=0: $\begin{matrix}{{kx} = {{\frac{{\varepsilon A}_{TOT}V^{2}}{2\left( {g - x} \right)^{2}}{or}\quad 2{{kx}\left( {g - x} \right)}^{2}} = {{\varepsilon A}_{TOT}V^{2}}}} & (3)\end{matrix}$

Define a constant C=2k/ε, so that the above becomes:Cx(g−x)² =A _(TOT) V ²  (4)

In one application of Eq. (4), one can keep the voltage V constant andadjust the area A_(TOT) by activating only some subset of the electrodesegments A_(n). In such a case, solving Eq. (4) for the required A_(TOT)as a function of desired displacement x results in $\begin{matrix}{A_{TOT} = {{\frac{C}{V^{2}}{x\left( {g - x} \right)}^{2}} = {\frac{C}{V^{2}}\left\lbrack {x^{3} - {2{gx}^{2}} + {g^{2}x}} \right\rbrack}}} & (5)\end{matrix}$This relationship is nonlinear and is undesirable for the reasonsdescribed previously. A desirable condition is one in which thedisplacement x is linearly proportional to the activation area A_(TOT),i.e., dx/dA, and therefore dA/dx, are constant. Taking the derivative ofEq. (5) with respect to x leads to $\begin{matrix}{\frac{dA}{dx} = {\frac{C}{V^{2}}\left\lbrack {{3x^{2}} - {4{gx}} + g^{2}} \right\rbrack}} & (6)\end{matrix}$Taking this equation's reciprocal results in: $\begin{matrix}{\frac{dx}{dA} = \frac{V^{2}}{C\left( {{3x^{2}} - {4{gx}} + g^{2}} \right)}} & (7)\end{matrix}$

One can then impose the additional constraint that V also be a functionof the desired displacement x. Specifically, let V(x)=V_(o)(g−x)/g,where V_(o) is the value of V at zero displacement, and where V isreduced as x approaches in value that of the gap spacing, g. Thedisplacement equation, now a function of both area A_(TOT) and appliedvoltage V(x), becomes: $\begin{matrix}{A_{TOT} = {{\frac{C}{V^{2}}{x\left( {g - x} \right)}^{2}} = {{\frac{gC}{{V_{0}^{2}\left( {g - x} \right)}^{2}}{x\left( {g - x} \right)}^{2}} = {\frac{gC}{V_{0}^{2}}x}}}} & (8)\end{matrix}$The displacement x then becomes $\begin{matrix}{x = \frac{V_{0}^{2}A_{TOT}}{gC}} & (9)\end{matrix}$

FIG. 7 illustrates an overall digital bit application system for use inthe present invention. Voltage from a command system 120 is appliedthrough and converted in a processor 121 which may be hard- or softwareoperated, to apply a digital word 122 to a distribution system 124 whichapplies on busses 130, 132 . . 134, voltages representing the binarybits 0 or 1 in some combination to individual actuators 140. The busses130-134 will typically contain multiple leads for the individualelectrode segments to be activated as illustrated above with respect toFIG. 5.

The above-described preferred embodiment is intended as exemplary only,the scope of the invention being described and limited only as shown inthe following claims.

1. A micromechanical apparatus having one or more electronicallyadjustable structures comprising: a set having: a first electrodesupported on a substrate; a second electrode supported substantiallyparallel from said first electrode, said second electrode being movablewith respect to said first electrode whereby an electric potentialapplied between said first and second electrodes causes said secondelectrode to move toward said first electrode distance X, (X), where Xis a nonlinear function of said potential, (V) and V is a representationof a desired value of X; and means for linearizing the relationshipbetween V and X.
 2. The apparatus of claim 1 wherein one of said firstand second electrodes is divided into n plural separate electrodesegments which increase from a first area over which said force resultsto a final larger, nth such area according to a predetermined geometricprogression which offsets the nonlinearization in said transfer functionbetween X and V.
 3. The apparatus of claim 2 wherein said nonlinearprogression produces a doubling in the area between each segment fromsaid first electrode segment area through each successive electrodesegment to said nth electrode segment area thereby providing a secondorder adjustment in the transfer function between displacement X andapplied potential V.
 4. The apparatus of claim 1, wherein a plurality ofsets of said first and second electrodes are arranged in atwo-dimensional array.
 5. The apparatus of claim 1 further comprising areflective element supported by said second electrode substantially at apoint of maximum deflection thereof in response to said appliedpotential.
 6. The apparatus of claim 5 including means for applying apotential between first and second electrodes operative to reflectradiation over a range of angles corresponding to the deflection of eachof said second electrodes in said array through phase delay wavefrontsteering.
 7. The apparatus of claim 5 including means for applying apotential between said first and second electrodes operative to reflectradiation over a range of phase adjustments corresponding to thedeflection of each of said second electrodes in said array throughdelayed phase reflection.
 8. The apparatus of claim 1 wherein saidlinearizing means further includes means for applying said potential, V,to selected ones of said electrode segments.
 9. The apparatus of claim 1wherein said means for linearizing includes means for varying theapplied potential as a function of gap between said first and secondelectrodes.
 10. The apparatus of claim 9 wherein said means for varyingcauses said potential to decrease as the spacing between said first andsecond electrodes decreases.
 11. The apparatus of claim 6 wherein: saiddrive means further includes means for applying said potential, V, toselected ones of said electrode segments; and means for varying thevoltage applied to said electrode segments are provided to increase thevoltage between said first and second electrodes in synchronism with theapplication thereof to respective ones of said electrode segments. 12.The apparatus of claim 11 wherein said drive means includes means forcontrolling the application of said potential to each electrode segmentaccording to states of digital bits of a digital signal.
 13. Theapparatus of claim 10, further including means for varying the voltageapplied to said electrode segments as a function of induced displacementcomprising a plurality of current sources individually activated bydigital signals synchronized to the activation of each of said pluralityof segments, said current source increasing in magnitude from a firstcurrent level, corresponding to activation of said first electrodesegment to an nth current level corresponding to activation of an nthelectrode segment with each sequential current source differing fromeach other by a factor divisible by 2 in a monotonically increasingseries from said first electrode segment associated current source tosaid nth electrode segment associated current source.
 14. A method forcontrolling the reflection of light from a plurality of reflectivesurfaces positionally controlled by an array of micromechanicalactuators each comprising first and second spaced electrodes, at leastone of which comprises a plurality of electrode segments, by wavefrontdelay according to displacement of each of said reflective elements insaid array, said method comprising: applying a potential to each of saidfirst and second electrodes by selective activation of electrodesegments thereof according to an intended displacement in a manner tolinearize a transfer function between said potential and saiddisplacement.
 15. The method of claim 14 further including the step ofvarying the potential applied to said first and second electrodeslinearly as a function of an intended displacement thereof.
 16. Amicromechanical apparatus having one or more electronically steerablestructures comprising: a set having: a first electrode supported on asubstrate; a second electrode supported substantially parallel from saidfirst electrode, said second electrode being flexible with respect tosaid first electrode whereby an electric potential applied between saidfirst and second electrodes causes said first and second electrodes tomove relative to each other a distance X, (X), where X is a nonlinearfunction of said potential, (V); and means for linearizing therelationship between V and X.
 17. The apparatus of claim 3, wherein aplurality of sets of said first and second electrodes are arranged in atwo-dimensional array.
 18. The apparatus of claim 17 further comprisinga reflective element supported by said second electrode substantially ata point of maximum deflection thereof in response to said appliedpotential.
 19. The apparatus of claim 18 including means for applying apotential between first and second electrodes operative to reflectradiation over a range of angles corresponding to the deflection of eachof said second electrodes in said array through phase delay wavefrontsteering.
 20. The apparatus of claim 18 including means for applying apotential between said first and second electrodes operative to reflectradiation over a range of phase adjustments corresponding to thedeflection of each of said second electrodes in said array throughdelayed phase reflection.
 21. The apparatus of claim 19 wherein saidlinearizing means further includes means for applying said potential, V,to selected ones of said electrode segments.
 22. The apparatus of claim20 wherein said linearizing means further includes means for applyingsaid potential, V, to selected ones of said electrode segments.
 23. Theapparatus of claim 21 wherein said means for linearizing includes meansfor varying the applied potential as a function of gap between saidfirst and second electrodes.
 24. The apparatus of claim 22 wherein saidmeans for linearizing includes means for varying the applied potentialas a function of gap between said first and second electrodes.
 25. Theapparatus of claim 23 wherein said means for varying causes saidpotential to decrease as the spacing between said first and secondelectrodes decreases.
 26. The apparatus of claim 24 wherein said meansfor varying causes said potential to decrease as the spacing betweensaid first and second electrodes decreases.
 27. The apparatus of claim19 wherein: said drive means further includes means for applying saidpotential, V, to selected ones of said electrode segments; and means forvarying the voltage applied to said electrode segments are provided toincrease the voltage between said first and second electrodes insynchronism with the application thereof to respective ones of saidelectrode segments.
 28. The apparatus of claim 25, further includingmeans for varying the voltage applied to said electrode segments as afunction of induced displacement comprising a plurality of currentsources individually activated by digital signals synchronized to theactivation of each of said plurality of segments, said current sourceincreasing in magnitude from a first current level, corresponding toactivation of said first electrode segment to an nth current levelcorresponding to activation of an nth electrode segment with eachsequential current source differing from each other by a factordivisible by 2 in a monotonically increasing series from said firstelectrode segment associated current source to said nth electrodesegment associated current source.
 29. The apparatus of claim 26,further including means for varying the voltage applied to saidelectrode segments as a function of induced displacement comprising aplurality of current sources individually activated by digital signalssynchronized to the activation of each of said plurality of segments,said current source increasing in magnitude from a first current level,corresponding to activation of said first electrode segment to an nthcurrent level corresponding to activation of an nth electrode segmentwith each sequential current source differing from each other by afactor divisible by 2 in a monotonically increasing series from saidfirst electrode segment associated current source to said nth electrodesegment associated current source.
 30. The apparatus of claim 11,further including means for varying the voltage applied to saidelectrode segments as a function of induced displacement comprising aplurality of current sources individually activated by digital signalssynchronized to the activation of each of said plurality of segments,said current source increasing in magnitude from a first current level,corresponding to activation of said first electrode segment to an nthcurrent level corresponding to activation of an nth electrode segmentwith each sequential current source differing from each other by afactor divisible by 2 in a monotonically increasing series from saidfirst electrode segment associated current source to said nth electrodesegment associated current source.
 31. The apparatus of claim 12,further including means for varying the voltage applied to saidelectrode segments as a function of induced displacement comprising aplurality of current sources individually activated by digital signalssynchronized to the activation of each of said plurality of segments,said current source increasing in magnitude from a first current level,corresponding to activation of said first electrode segment to an nthcurrent level corresponding to activation of an nth electrode segmentwith each sequential current source differing from each other by afactor divisible by 2 in a monotonically increasing series from saidfirst electrode segment associated current source to said nth electrodesegment associated current source.